Question

A black body is heated from $7^{\circ }C$ to ${287}^{\circ }C$. The ratio of radiation emitted is

• A. $1:256$
• B. $1:64$
• C. $1:16$
• D. $1:27$

Answer 1

The correct option is C $1:16$

Given: Initial temperature,

$T_1=7^{\circ }C=280K$
Final temperature,
$T_2={287}^{\circ }C=560K$

According, the Stefan’s law the radiated energy is given by
$E\propto T^4$
Hence,

$\frac{E_1}{E_2}=\frac{T_1^4}{T_2^4}={\left(\frac{280}{560}\right)}^4=\frac{1}{16}$

$E_1:E_2=1:16$